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302 PAÑCASIDDHĀNTIKĀ XVII.7 True planets The first step 4. Deduct the mean from the śīghra. If the remainder (called śīghra-kendra) is within 90°, sin. śīghra-kendra is called bhuja, and sin (90° – śīghra-kendra) is called koṭi. If śīghra-kendra is more than 90° and less than 180°, subtract it from 180°. (Taking this as the śīghra-kendra, sin. śīghra-kendra is bhuja and sin (180° – śīghra-kendra) is koṭi. If śīghra-kendra is more than 180° and less than 270°, deduct 180° from it and take this as śīghra-kendra. Sin. śīghra-kendra is bhuja and sin (90° – śīghra-kendra) is koṭi. If śīghra-kendra is from 270° to 360°, deduct it from 360° and take its sine as the bhuja and sin 90° – śīghra-kendra is the koṭi. (The bhuja of manda-kendra is to be found in the same way using manda-kendra in the place of śīghra-kendra)¹ 5-6. The bhuja and koṭi must be multiplied by the planet’s epicycle of conjunc- tion and divided by 360. Thus transformed, they are called bhuja-result and koṭi-result pertaining to the equation of conjunction. If the śīghra-madhya is from 270° to 90°, the koṭi-result is to be added to 120 (the R. of the PS). If śīghra-madhya is from 90° to 270°, the koṭi-result is to be subtracted from 120. Square this and add it to the square of the bhuja-result. Find its square root, and by this divide 120 × bhuja-result. Find arc-sine of this. Subtract half this from the longitude of apsis if the śīghra-kendra is from 0° to 180°. Add if from 180° to 360°. स्फुटयित्वैवं मन्दं मध्याच्च विशोध्य तस्य भुजम् । परिणाम्य कार्मुकार्धं तन्मन्देनैव धनहानी ॥ ७ ॥ Second step 7. Half rectifying the apogee position thus, deduct it from the mean. The result is to be used as the anomaly of the apsis in the second step. As we find the bhuja of the anomaly of conjunction (śīghra-kendra) so find the bhuja of the anomaly of apsis. Multiply the bhuja by the manda epicycle and divide by 360. and get the transformed bhuja-result of the apsis. (This is sine equation of the 4.5. Quoted by Utpala on BS, 2. pp. 44-45 d. A1. षड्भ्याः; B.C.D.U. षड्भ्यः A.B. पतते 4a. U. मध्यविहीनाद् 5b. A. गुणैर्विपगते तच्च; B. गुणे वियुगतक्ष; b. A. वाशित्रितये A.B. गतैष्व (B2.3. ष्य) C.D. गुणैर्विप [रि] णते तच्च (D. णते ते ततश्च) A.B. ॰दंशे ज्ये; U. ॰दंशज्या d. B. कर्कादौ A.B. चयापचयाः; U. चयापचयः c. B. कोटि ———————————————————————————————————————————————————————————————— ¹ In modern usage, for all the above we can simply say sin. śīghra-kendra is the bhuja and cos. śīghra-kendra is the koṭi, without taking into account the sign + or −.)